This invention pertains to apparatus and methods employed for determining residual stress on polycrystalline samples by X-ray diffraction.
X-ray diffraction has been long established and is the only known, generally accepted, nondestructive method for determining residual stress on polycrystalline samples. When a collimated beam of monochromatic X-ray radiation impinges upon the surface of a polycrystalline sample, a number of cones of diffracted radiation are formed which extend and expand outwardly from the surface of the sample. For one of these cones, the angle by which the incident X-ray beam is deflected is called the scattering angle and is indicated by 2.theta.. The scattering of radiation is due to a particular set of internal crystallographic planes having spacing d, and the diffraction condition is expressed by the so-called Bragg law: EQU .lambda.=2d sin .theta.
wherein .lambda. is the wavelength of the incident X-ray beam.
The normal to the family of crystallographic planes responsible for the diffraction of the incident X-ray beam forms an angle .psi. with the normal to the surface of the polycrystalline sample. The projection of this normal into the plane of the sample's surface forms an angle .phi. with a reference direction on said surface. Thus, the normal to the diffracting planes is identified by the angles .phi. and .psi..
Measurement of the scattering angle 2.theta. provides a determination of the interplanar spacing d in the direction of the normal to the diffracting planes. If a state of stress is present in the sample, the angle 2.theta. changes slightly with the orientation of the crystallographic planes and, because this orientation is defined by the angles .psi. and .phi., it is indicated as 2.theta..sub..phi.,.psi.. For the purpose of stress measurements, it is sufficient to measure the variation of the scattering angle with .phi. and .psi. from a reference value, or .DELTA.2.theta..sub..phi.,.psi..
The determination of the stress at the surface of the sample by X-ray diffraction requires first directing a collimated monochromatic beam of X-rays onto the surface of the sample, and then determining the function .DELTA.2.theta..sub..phi.,.psi. for some values of .phi. and .psi.. It is then possible to derive the stress field in the irradiated area from the function .DELTA.2.theta..sub..phi.,.psi..
In most cases the state of stress is sufficiently defined by a biaxial system of stresses parallel to the surface of the specimen, and the elastic behavior of the sample is substantially isotropic. In this situation the measurement of only two values of .DELTA.2.theta..sub..phi.,.psi. at different angles .psi. for constant angle .phi. is sufficient to allow the determination of the component of stress in the direction of angle .phi..
Two methods are currently employed for determining the function .DELTA.2.theta..sub..phi.,.psi.. The first is the so-called diffractometer method which utilizes a narrow-slit detector. The detector is attached to a rotating arm connected for pivotal movement around the point where the incident beam impinges upon the surface of the sample. The diffractometer measures angles directly, and the scattering angle is determined by finding the point of maximum intensity as the detector and arm rotate. The second method is the so-called position sensitive detector method. In this method the detector and its associated electronics provide information concerning the intensity of the radiation falling upon the detector as a function of position. In order to transform the positional information into angular information, the sample-to-detector distance must be very accurately predetermined. Because the variations in .DELTA.2.theta..sub..phi.,.psi. which are produced by stress on the sample are very small, even small errors in the distance measurement can not be tolerated.
Diffractometers and position sensitive detectors of the prior art are basically one-dimensional, i.e.--they are capable of detecting only a relatively minute portion of the diffraction cone periphery. They are also usually designed to perform measurements of .DELTA.2.theta..sub..phi.,.psi. at constant angle .phi. and variable angle .psi.. One drawback associated with these systems is the difficulty encountered in using them to determine residual stress upon polycrystalline samples having surface grains of dimensions which tend to produce spotty diffraction rings on a conventional film exposure, such as, for example, 0.015-0.050 mm grain size in quartz powder using CuK.sub..alpha. X-rays. A still further drawback resides in the fact that only one determination of residual stress in a given direction can be made at a time. For example, the stress component in the direction of the longitudinal axis of the sample can be first determined. Then, a determination of the transverse residual stress component is made by rotating either the sample or detector 90.degree. about an axis perpendicular to the sample surface and while maintaining constant the sample-to-detector distance.
In view of the foregoing drawbacks associated with the prior art, an object of this invention is to provide a means and method for accurately determining mutually orthogonal residual stress components on a polycrystalline sample without the necessity of having to rotate the sample relative to the detector.
Another object of this invention is to provide a means and method wherein accurate prior knowledge of the sample-to-detector distance is not critical for determining the residual stress.
A still further object of this invention is to provide means and method which is usable with polycrystalline materials exhibiting a tendency to produce spotty diffraction rings because of relatively large surface grain dimensions.